Explanation

(c) Let the radii of the thin spherical and the solid sphere are $R_{1}$ and $R_{2}$ respectively.
Then the moment of inertia of the spherical shell about their diameter
$I = \frac{2}{3}\ MR_{1}^{2}$ …(i)
and the moment of inertia of the solid sphere is given by
$I = \frac{2}{5}MR_{2}^{2}$ …(ii)
Given that the masses and moment of inertia for both the bodies are equal, then from Eqs. (i) and (ii)
$\frac{2}{3}MR_{1}^{2} = \frac{2}{5}MR_{2}^{2} \Rightarrow \frac{R_{1}^{2}}{R_{2}^{2}} = \frac{3}{5}$
$\Rightarrow$ $\frac{R_{1}}{R_{2}} = \sqrt{\frac{3}{5}}\ \Rightarrow R_{1}:R_{2} = \sqrt{3}:\sqrt{5}$